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The operation delta is defined for all nonzero x and y b x

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The operation delta is defined for all nonzero x and y b x [#permalink] New post 29 Jul 2007, 10:56
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D
E

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92% (01:47) correct 7% (01:20) wrong based on 14 sessions
The operation # is defined for all nonzero x and y by x#y = x + x/y. If a>0, then 1#(1#a) =

A. a
B. a+1
C. a/(a+1)
D. (a+2)/(a+1)
E. (2a+1)/(a+1)

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-operation-is-defined-for-all-nonzero-x-and-y-by-x-y-162019.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Jan 2014, 04:03, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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 [#permalink] New post 29 Jul 2007, 12:53
(E) for me :)

o 1 delta a
= 1 + 1/a
= (a + 1)/a

o 1 delta (1 delta a)
= 1 delta ((a + 1)/a)
= 1 + 1/((a + 1)/a)
= 1 + a/(a+1)
= (2*a + 1) / (a + 1)
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 [#permalink] New post 30 Jul 2007, 22:39
1 delta a = 1 + 1/a
Let 1 delta a be x

Then 1 delta (1 delta a) = 1 delta x = 1 + 1/x. Subsitute in x, to give

1 + 1/(1+1/a) = 1 + a/(a+1) = a+1+a/(a+1) = 2a+1/(a+1)
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Re: The operation delta is defined for all nonzero x and y b x [#permalink] New post 02 Jan 2014, 07:26
Can someone explain the math better on this one? Brunnel, do you mind?
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Re: The operation delta is defined for all nonzero x and y b x [#permalink] New post 03 Jan 2014, 04:04
Expert's post
jeremyl3763 wrote:
Can someone explain the math better on this one? Brunnel, do you mind?


The operation # is defined for all nonzero x and y by x#y = x + x/y. If a>0, then 1#(1#a) =
A. a
B. a+1
C. a/(a+1)
D. (a+2)/(a+1)
E. (2a+1)/(a+1)

1#(1#a) = 1#(1+\frac{1}{a}) = 1#(\frac{a+1}{a})= 1+ \frac{1}{(\frac{a+1}{a})}=1+\frac{a}{a+1}=\frac{a+1+a}{a+1}=\frac{2a+1}{a+1}.

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-operation-is-defined-for-all-nonzero-x-and-y-by-x-y-162019.html
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Re: The operation delta is defined for all nonzero x and y b x [#permalink] New post 03 Jan 2014, 04:04
Expert's post
Bunuel wrote:
jeremyl3763 wrote:
Can someone explain the math better on this one? Brunnel, do you mind?


The operation # is defined for all nonzero x and y by x#y = x + x/y. If a>0, then 1#(1#a) =
A. a
B. a+1
C. a/(a+1)
D. (a+2)/(a+1)
E. (2a+1)/(a+1)

1#(1#a) = 1#(1+\frac{1}{a}) = 1#(\frac{a+1}{a})= 1+ \frac{1}{(\frac{a+1}{a})}=1+\frac{a}{a+1}=\frac{a+1+a}{a+1}=\frac{2a+1}{a+1}.

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-operation-is-defined-for-all-nonzero-x-and-y-by-x-y-162019.html


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Hope this helps.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The operation delta is defined for all nonzero x and y b x   [#permalink] 03 Jan 2014, 04:04
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